 About 3,320 results  books.google.com Quadratic Transformations The formulas 3.8(1—24) may be viewed as a
transformation of the 2F1 in the variable, actually a linear ... The basic formulas
are due to Gauss and Kummer and a complete list is due to Goursat; see Erdélyi
et al. 

 books.google.com 1662 Kummer's Function where 2F1(a, b, c, z) is the HYPERGEOMETRIC
FUNCTION with m #–1/2, 1, 3/2, ..., and T(z) is the ... Kummer's Function
CONFLUENT HYPERGEOMETRIC FUNCTION Kummer's Quadratic
Transformation A ... 

 books.google.com In order to relate them to each other, we must use Kummer's quadratic
transformation formula. This involves certain substitutions which lift the
correlation functions of t — Z2/zi to functions of x on a foursheeted covering of
the sphere, branched ... 

 books.google.com 8.18 Show that 2/ r(i[c + a])r(i[ca+ 1]) .19 Use (8.6.23) (with a and b interchanged
) to derive Kummer's quadratic transformation (6.1.11). .20 Show that / 1 1\ r(i[a +
*+l])r(i) F[a,b,[a + b+l]; » 2 2/ r(I[fl+l])r(I[6+l]) 8.21 Verify the identity (8.4.5). 

 books.google.com Quadratic Transformations In §5.4 we mentioned Kummer's 24 solutions of the
hypergeornetric differential equation. ... (1881) made a thorough study of another
kind of transformation, although the basic ideas are due to Gauss and Kummer. 

 books.google.com Bruce C. Berndt, Robert Alexander Rankin  2001  Preview At the end of the second part of this paper Kummer wrote that he had tried to
extend his results to ... The rest of the quadratic transformations come from using
linear fractional relations and connections between three solutions of the ... 

 books.google.com (6,202) 2 4x3 Kummer's quadratic transformation formulas for the hypergeometric
functions give (see [1], 15.3.22) 1 1 Fi  –2 ji , –2 j2; – — ji – j2; —— 2 ( J1 J25 2
J1  J2 :) 1 1 \* = 2 Fl (    ( #) ) • (6.203) 2 2x3 Now for any 6 Ji ..J2 ji y y  • y ... 

 books.google.com Linear, Quadratic and Cubic Transformations PfajfKummer transformations: 2F1
<a, b; C; 1) = (1—Z)—a2F1 (4, cb; C; L) <19) z—1 (c<,:25; arg(1—z) §7T—€ (0
<€ <rr)); 2F1<a, b; C; 1) = <1 Z)_b2F1 <1», c 4; C; <20) Z (c˘Z6; arg(1—z) ... 

 books.google.com In Pfaff 's transformation, 2Fi[a'f:X)=(lX)b2Fi(b'\a,^), (2.2.6) change x to x/b and
let b — > oo to get Kummer's first transformation, lFl(acx\=e\Fl(C~Ux\ (4.1.11) A
similar procedure applied to the quadratic transformation, a>b. 4x \ „ . x2a r ... 

 books.google.com 208 — 211 Relation of the transformation to the theory of Kummer's surface 211,
212 Rummer's quartic surface as the ... 230 — 234 The rationality of the
Quadratic Complex, and of the Quadratic Congruence 234—237 The generation
of a ... 

 